{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:BJ6UTTYZXCHLUY7H4UVWFLKC3N","short_pith_number":"pith:BJ6UTTYZ","schema_version":"1.0","canonical_sha256":"0a7d49cf19b88eba63e7e52b62ad42db4f420fbbbeafd89d01d07f66199c7648","source":{"kind":"arxiv","id":"1503.00091","version":1},"attestation_state":"computed","paper":{"title":"Efficient Domination for Some Subclasses of $P_6$-Free Graphs in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Andreas Brandst\\\"adt, Elaine M. Eschen, Erik Friese","submitted_at":"2015-02-28T07:24:17Z","abstract_excerpt":"Let $G$ be a finite undirected graph. A vertex {\\em dominates} itself and all its neighbors in $G$. A vertex set $D$ is an {\\em efficient dominating set} (\\emph{e.d.}\\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \\emph{Efficient Domination} (ED) problem, which asks for the existence of an e.d.\\ in $G$, is known to be \\NP-complete even for very restricted graph classes such as $P_7$-free chordal graphs. The ED problem on a graph $G$ can be reduced to the Maximum Weight Independent Set (MWIS) problem on the square of $G$. The complexity of the ED proble"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1503.00091","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2015-02-28T07:24:17Z","cross_cats_sorted":[],"title_canon_sha256":"f29c38befb305b0d0f0663f14452590394cc43dd8ab402a7a515060ce4a71b9f","abstract_canon_sha256":"b01c672b7bf9fbdfc324ba45f64022df14cc68cd7ad98c9ea576591088d8cd02"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:25:55.166081Z","signature_b64":"yT8Jvk7AfjA7N0QxHwsJ+TojJ6euOmmtINUN8pPd6l8WLfTe1wDufvmfsEMy//HL3qbDfQcffc0jE7KgXlenBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0a7d49cf19b88eba63e7e52b62ad42db4f420fbbbeafd89d01d07f66199c7648","last_reissued_at":"2026-05-18T02:25:55.165641Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:25:55.165641Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Efficient Domination for Some Subclasses of $P_6$-Free Graphs in Polynomial Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"Andreas Brandst\\\"adt, Elaine M. Eschen, Erik Friese","submitted_at":"2015-02-28T07:24:17Z","abstract_excerpt":"Let $G$ be a finite undirected graph. A vertex {\\em dominates} itself and all its neighbors in $G$. A vertex set $D$ is an {\\em efficient dominating set} (\\emph{e.d.}\\ for short) of $G$ if every vertex of $G$ is dominated by exactly one vertex of $D$. The \\emph{Efficient Domination} (ED) problem, which asks for the existence of an e.d.\\ in $G$, is known to be \\NP-complete even for very restricted graph classes such as $P_7$-free chordal graphs. The ED problem on a graph $G$ can be reduced to the Maximum Weight Independent Set (MWIS) problem on the square of $G$. The complexity of the ED proble"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00091","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1503.00091","created_at":"2026-05-18T02:25:55.165726+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.00091v1","created_at":"2026-05-18T02:25:55.165726+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.00091","created_at":"2026-05-18T02:25:55.165726+00:00"},{"alias_kind":"pith_short_12","alias_value":"BJ6UTTYZXCHL","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_16","alias_value":"BJ6UTTYZXCHLUY7H","created_at":"2026-05-18T12:29:14.074870+00:00"},{"alias_kind":"pith_short_8","alias_value":"BJ6UTTYZ","created_at":"2026-05-18T12:29:14.074870+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N","json":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N.json","graph_json":"https://pith.science/api/pith-number/BJ6UTTYZXCHLUY7H4UVWFLKC3N/graph.json","events_json":"https://pith.science/api/pith-number/BJ6UTTYZXCHLUY7H4UVWFLKC3N/events.json","paper":"https://pith.science/paper/BJ6UTTYZ"},"agent_actions":{"view_html":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N","download_json":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N.json","view_paper":"https://pith.science/paper/BJ6UTTYZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.00091&json=true","fetch_graph":"https://pith.science/api/pith-number/BJ6UTTYZXCHLUY7H4UVWFLKC3N/graph.json","fetch_events":"https://pith.science/api/pith-number/BJ6UTTYZXCHLUY7H4UVWFLKC3N/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N/action/storage_attestation","attest_author":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N/action/author_attestation","sign_citation":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N/action/citation_signature","submit_replication":"https://pith.science/pith/BJ6UTTYZXCHLUY7H4UVWFLKC3N/action/replication_record"}},"created_at":"2026-05-18T02:25:55.165726+00:00","updated_at":"2026-05-18T02:25:55.165726+00:00"}